Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / Section A / A1 / b

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- Solution b

Solution

Wavefunction normalization cancels in the ratio of integrals:

P (a /2 < x < a) = \frac{\int _{a /2}^{a} ( a ^{2} + x ^{2} ) d x}{\int _{0}^{a} ( a ^{2} + x ^{2} ) d x} = \frac{19 a ^{3} /24}{4 a ^{3} /3} = \frac{19}{32} .

A normalized version of the specified wavefunction is

3 (a + i x) / (2 a^{3/2})

on its support.

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